A) \[{{\cos }^{-1}}\left( \frac{7}{31} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{9}{35} \right)\]
Correct Answer: C
Solution :
Here, \[\overrightarrow{OP}\times \overrightarrow{OQ}=(\hat{i}+2\hat{j}+\hat{k})\times (2\hat{i}+\hat{j}+3\hat{k})\] \[=5\hat{i}-\hat{j}-3\hat{k}\] Again,\[\overrightarrow{PQ}\times \overrightarrow{PR}=(\hat{i}-\hat{j}+2\hat{k})\times (-2\hat{i}-\hat{j}+\hat{k})\] \[=\hat{i}-5\hat{j}-3\hat{k}\] Let angle between faces OPQ and PQR is \[\theta \] \[\therefore \] \[\cos \theta =\frac{5+5+9}{{{(\sqrt{25+9+1})}^{2}}}=\frac{19}{35}.\]You need to login to perform this action.
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